Self-Learning Modules in
Mathematics
Quarter 1 Week 4 - 8
SDO MALABON CITY
7
GOVERNMENT PROPERTY
NOT FOR SALE
PROJECT MIMs Grade 7
G7 MIMs # 12 – WEEK 4 – 1
st
QUARTER
CONVERTING FRACTION TO DECIMAL
Rational numbers like
,
,
, and
are common fractions or simply fractions.
The fraction line separating the two numbers indicates division. The integer
above the fraction line is the numerator (dividend) and the integer below is
the denominator (divisor). The numerator and the denominator are the terms
of a fraction.
In converting fractions to decimals, we can use long division.
Examples
1. What is
as decimal?
2. What is
as decimal?
0
.
6
2
5
5
.
0
0
0
4
8
2
0
1
6
4
0
4
0
0
0
.
7
5
3
.
0
0
2
8
2
0
2
0
0
LEARNING COMPETENCY - Express rational numbers from fraction form
to decimal form and vice versa.
OBJECTIVE: Convert fraction to decimal.
-
-
-
-
-
Therefore,

Therefore,

92
PROJECT MIMs Grade 7
Convert each fraction to decimal. Write your answer on a separate sheet of
paper. Show your complete solution.
1.
4.

2.
5.

3.


Reinforcement
Choose the letter of the correct answer. Then write it on a separate sheet of paper.
1. What is the decimal equivalent of


?
A. 0.400 B. 0.425 C.0.450 D. 0.475
2. What is the decimal equivalent of


?
A. 0.145 B. 0.148 C.0.150 D. 0.152
3. Which fractions have the smallest decimal equivalent?
A.
B.
C.
D.


4. Which fractions have the largest decimal equivalent?
A.
B.
C.
D.


5. The teacher asked Sam and Andrei to convert

to fraction, and
Sam’s answer is 0.056 while Andrei’s answer is 0.0056. What can you
say about Sam and Andrei’s answers?
A. Sam and Andrei’s answers are both wrong.
B. Sam and Andrei’s answers are both correct.
C. Sam’s answer is correct while Andrei’s answer is wrong.
D. Sam’s answer is wrong while Andrei’s answer is correct.
CHALLENGE
Read and analyze the given problem. Write your answer on a separate sheet of
paper. Show your complete solution.
What is the sum of all the sides of the rectangle?
1. Express the answer in decimal.
2. Gab’s teacher asked him to add the fractions
and

. This was Gab’s answer:


Express Gab's answer in decimal form to see whether or not he was correct.
1.5 m
m
93
PROJECT MIMs Grade 7
G7 MIMs # 13 – WEEK 4 – 1
st
QUARTER
CONVERTING DECIMAL TO FRACTION
To convert a decimal to a fraction follow these steps:
Step 1: Write down the decimal divided by 1, like this:
decimal
1
Step 2: Multiply both numerator and denominator by 10 for every number
after the decimal point. (For example, if there are two numbers after the
decimal point, then use 100, if there are three then use 1000, etc.)
Step 3: Simplify or reduce the fraction.
RECALL:
Simplifying (or reducing) fractions means to make the fraction as simple as
possible.
How do I simplify a fraction?
Divide both the top and bottom of the fraction by the Greatest Common
Factor.
Examples:
Simplify
4
12
÷
4
4
=
1
3
Simplify
36
90
÷
9
9
=
4
10
Simplify
24
120
÷
8
8
=
3
15
Examples
1. Convert 0.625 into fraction
Step 1 =
0.625
1
Step 2 = (
0.625
1
) × =
625
1000
Step 3 =
625
1000
÷ =
25
40
÷ =
5
8
Therefore 0.625 =
5
8
LEARNING COMPETENCY - Express rational numbers from fraction form to
decimal form and vice versa.
OBJECTIVE: Convert decimal to fraction.
1000
1000
25
25
5
5
94
PROJECT MIMs Grade 7
2. Convert 0.75 into fraction
Step 1 =
0.75
1
Step 2 = (
0.75
1
) ×
100
100
=
75
100
Step 3 =
75
100
÷
25
25
=
3
4
Therefore, 0.75 =
3
4
Convert each decimal to fraction. Express the answer in lowest term. Write your
answer on a separate sheet of paper. Show your complete solution.
1. 0.7 6. 0.368
2. 0.8 7. 0.072
3. 0.24 8. 0.394
4. 0.65 9. 0. 856
5. 0.98 10. 0.6532
Reinforcement
Choose the letter of the correct answer. Then write it on a separate sheet
of paper.
1. What is 0.85 as a fraction in lowest term?
A.
17
20
B.
17
25
C.
19
20
D.
19
25
2. What is 0.64 as a fraction in lowest term?
A.
3
5
B.
4
5
C.
16
25
D.
17
25
3. What is the fraction equivalent in lowest term of 0.425?
A.
9
20
B.
17
40
C.
19
40
D.
21
50
4. What is the fraction equivalent in lowest term of 0.82?
A.
40
50
B.
41
50
C.
42
50
D.
43
50
5. The sum 0.35 + 0.125 = 0.475, what is the fraction equivalent of the
given equation?
A.
3
5
+
1
25
=
4
75
C.
7
20
+
1
8
=
19
40
B.
7
20
+
1
8
=
8
28
D.
7
40
+
1
8
=
19
20
95
PROJECT MIMs Grade 7
CHALLENGE
Read and analyze the given problem. Write your answer on a separate sheet of
paper. Show your complete solution.
The teacher asked Paul and Abby to convert 0.125 to decimal in lowest term,
Paul’s answer is
1
8
while Abby’s answer is
1
4
. What can you say about Paul
and Abby’s answers?
96
PROJECT MIMs Grade 7
G7 MIMs # 13 – WEEK 4 – 1
st
QUARTER
CONVERTING DECIMAL TO FRACTION
To convert a decimal to a fraction follow these steps:
Step 1: Write down the decimal divided by 1, like this:
decimal
1
Step 2: Multiply both numerator and denominator by 10 for every number
after the decimal point. (For example, if there are two numbers after the
decimal point, then use 100, if there are three then use 1000, etc.)
Step 3: Simplify or reduce the fraction.
RECALL:
Simplifying (or reducing) fractions means to make the fraction as simple as
possible.
How do I simplify a fraction?
Divide both the top and bottom of the fraction by the Greatest Common
Factor.
Examples:
Simplify
4
12
÷
4
4
=
1
3
Simplify
36
90
÷
9
9
=
4
10
Simplify
24
120
÷
8
8
=
3
15
Examples
1. Convert 0.625 into fraction
Step 1 =
0.625
1
Step 2 = (
0.625
1
) × =
625
1000
Step 3 =
625
1000
÷ =
25
40
÷ =
5
8
Therefore 0.625 =
5
8
LEARNING COMPETENCY - Express rational numbers from fraction form to
decimal form and vice versa.
OBJECTIVE: Convert decimal to fraction.
1000
1000
25
25
5
5
97
PROJECT MIMs Grade 7
2. Convert 0.75 into fraction
Step 1 =
0.75
1
Step 2 = (
0.75
1
) ×
100
100
=
75
100
Step 3 =
75
100
÷
25
25
=
3
4
Therefore, 0.75 =
3
4
Convert each decimal to fraction. Express the answer in lowest term. Write your
answer on a separate sheet of paper. Show your complete solution.
1. 0.7 6. 0.368
2. 0.8 7. 0.072
3. 0.24 8. 0.394
4. 0.65 9. 0. 856
5. 0.98 10. 0.6532
Reinforcement
Choose the letter of the correct answer. Then write it on a separate sheet
of paper.
1. What is 0.85 as a fraction in lowest term?
A.
17
20
B.
17
25
C.
19
20
D.
19
25
2. What is 0.64 as a fraction in lowest term?
A.
3
5
B.
4
5
C.
16
25
D.
17
25
3. What is the fraction equivalent in lowest term of 0.425?
A.
9
20
B.
17
40
C.
19
40
D.
21
50
4. What is the fraction equivalent in lowest term of 0.82?
A.
40
50
B.
41
50
C.
42
50
D.
43
50
5. The sum 0.35 + 0.125 = 0.475, what is the fraction equivalent of the
given equation?
A.
3
5
+
1
25
=
4
75
C.
7
20
+
1
8
=
19
40
B.
7
20
+
1
8
=
8
28
D.
7
40
+
1
8
=
19
20
98
PROJECT MIMs Grade 7
CHALLENGE
Read and analyze the given problem. Write your answer on a separate sheet of
paper. Show your complete solution.
The teacher asked Paul and Abby to convert 0.125 to decimal in lowest term,
Paul’s answer is
1
8
while Abby’s answer is
1
4
. What can you say about Paul
and Abby’s answers?
99
PROJECT MIMs Grade 7
G7 MIMs # 14 – WEEK 5 – 1
st
QUARTER
OPERATION ON RATIONAL NUMBERS
Addition and Subtraction of Rational Numbers
In adding or subtracting similar fractions, add or subtract the numerator and
copy the common denominator and then simplify your answer.
Examples
1.

+

=


=


 and 
=

2.


=

=

and 
=

3.




=


= 

=

=

LEARNING COMPETENCY - Perform operations on rational numbers.
OBJECTIVE - Add and subtract similar fractions.
→ Add the numerators.
→ Change the sum to its lowest term by dividing the
numerator (top) and denominator (bottom) by the GCF.
→ Subtract the numerators.
→ Express the sum to its lowest term by dividing the
numerator and denominator by the GCF.
→ Add the numerators.
→ Change improper fraction into mixed number.
→ Simplify fraction into lowest term.
100
PROJECT MIMs Grade 7
4.

=

=
=
=
Find the sum or difference. Simplify your answer. Write your answer on a
separate sheet of paper. Show your complete solution.
1.
2.


3.


’
4.




5.




Reinforcement
Choose the letter of the correct answer. Then write it on a separate sheet
of paper.
1. Find the difference between

and

A.

B.


C.
D.
2. A pizza is divided into 8 equal parts each part is equal to
of the whole. If
you take away 2 slices of it, how much part of the whole pizza is left?
A.
B.
C.
D.
3. The length of a stick is


meters. It was broken into two smaller parts. If
one part measures


meters, how long is the other part?
A.


B.


C.
D.
4. Find the sum of
and
.
A.

B.
C.
D.
6.
7.




8.


9.



10.




→ Subtract the numerators.
→ Change improper fraction into mixed number.
→ Simplify fraction into lowest term.
101
PROJECT MIMs Grade 7
5. Amanda bought
kg. of candies and
kg. of chocolate. How many
kilograms did she bought all in all?
A.
B. 
C. 
D. 
CHALLENGE
Read and analyze the given problem. Write your answer on a separate
sheet of paper. Show your complete solution.
1. In

 

, what fraction should be in the box to make it a true
statement?
2. There are 4 whole pizzas, each divided into 8 equal parts. If
of the
pizza were eaten, how much pizza is left?
102
PROJECT MIMs Grade 7
G7 MIMs # 15 – WEEK 5 – 1
st
QUARTER
OPERATION ON RATIONAL NUMBERS
Addition and Subtraction of Rational Numbers
RULES IN ADDING/SUBTRACTION OF DISSIMILAR FRACTIONS
1. Make the denominators similar/same by finding the least common
multiple (LCM) of the denominators.
2. Rewrite each fraction to its equivalent fractions with a denominator that
is equal to the least common multiple (LCM) from step 1.
3. Add/subtract the new fractions from step 2. (Add/subtract the
numerators then copy the common/same denominators)
4. Always reduce the answer to its simplest form (lowest term).
Examples:
1. Addition of Dissimilar Fractions
Add:
Step 1: Make the denominators similar/same by finding the LCM of the
denominators.
List the multiples of the denominators.
Multiples of 3 = {3, 6, 9, 12…}
Multiples of 4 = {4, 8, 12…}
LCM = 12 (least common multiple)
Step 2: Rewrite each fraction to its equivalent fractions.
Step 3: Add the new fractions from step 2. (Add the numerators then copy
the common/same denominators)

+

=


LEARNING COMPETENCY - Perform operations on rational numbers.
OBJECTIVE - Add and subtract dissimilar fractions.
103
PROJECT MIMs Grade 7
Step 4: Always reduce the answer to its simplest form (lowest term).
List the factors of the numerator (13) and denominator (12)
Factors of 13 = {1, 13} Factors of 12 = {1, 2, 3, 4, 6, 12}
Common Factor: 1
GCF = 1 (Since the GCF of numerator and denominator is 1 then the
fraction is in the lowest term).
, Therefore, the sum is


2. Subtraction of Dissimilar Fractions
Subtract:
-
Step 1: Make the denominators similar/same by finding the LCM of the
denominators.
List the multiples of the denominators
Multiples of 6 = {6, 12, 18, 24…}
Multiples of 3 = {3, 6, 9…}
LCM = 6 (least common multiple)
Step 2: Rewrite each fraction to its equivalent fractions.
Step 3: Subtract the new fractions from step 2. (Subtract the numerators
then copy the common/same denominators)
-
=
Step 4: Always reduce the answer to its simplest form (lowest term).
List the factors of the numerator (3) and denominator (6)
Factors of 3 = {1, 3} Factors of 12 = {1, 2, 3, 6}
Common Factor: 1, 3
104
PROJECT MIMs Grade 7
GCF = 3 (Since the GCF of the numerator and the denominator is 1
the fraction is in the lowest term).
 =
, Therefore, the difference is
.
Find the sum or difference. Simplify your answer. Write your answer on a
separate sheet of paper. Show your complete solution.
1.
6.

-
2.
7.


-

3.
8.
4.
9.


5.

10.


Reinforcement
Choose the letter of the correct answer. Then write it on a separate sheet
of paper.
1. Which of the following is the sum of

in the lowest term?
A.


B.

C.

D.
2. Which fraction is equal to the difference of


?
A.

B.

C.


D.


3. Add
to
.
A.
B.
C.
D.
4. Subtract
from
.
A.

B.

C.


D.

5. What is the sum of
and
?
A.
B.
C.
D.
3
3
105
PROJECT MIMs Grade 7
CHALLENGE
Read and analyze the given problem. Write your answer on a separate
sheet of paper. Show your complete solution.
What fraction should be added to
to get

?
106
PROJECT MIMs Grade 7
G7 MIMs # 16 – WEEK 5 – 1
st
QUARTER
Multiplication and Division of Rational Numbers
In multiplying fraction, multiply the numerator by the numerator and
the denominator by the denominator then simplify the answer.
Examples
1.


=


=




42 ÷ 14 = 3 and 42 ÷ 14 = 5
=

2.


=


= 


= 




In dividing fractions, multiply the dividend by the multiplicative inverse
or reciprocal of the divisor.
Examples
1.



=


=




LEARNING COMPETENCY - Perform operations on rational numbers.
OBJECTIVE - Multiply and divide rational numbers.
→ Multiply both numerators.
→ Multiply both denominators.
→ Simplify fraction to lowest term by dividing both
numerator and denominator by the GCF.
→ Multiply both numerators.
→ Multiply both denominators.
→ Change improper fraction into mixed number.
→ Simplify fraction to lowest term by dividing both
numerator and denominator by the GCF.
24 ÷ 12 = 2 and 36 ÷ 12 = 3 .
→ Get the reciprocal of the divisor.
→ Multiply both numerators.
→ Multiply both denominators.
→ Simplify fraction to lowest term by dividing
both numerator and denominator by the GCF.
60 ÷ 20 = 3 and 140 ÷ 20 = 7.
107
PROJECT MIMs Grade 7
2.

=

=


24 ÷ 6 = 4 and 30 ÷ 6 = 5


=


=


=


I. Match the given in column A with their corresponding product in
column B. Write your answer on a separate sheet of paper. Show
your complete solution.
Column A
1.

2.

3.
4.



5.

Column B
A.
B.
C.
D.
E.
F.
G.
H. 
→ Get the reciprocal of the divisor.
→ Multiply both numerators.
→ Multiply both denominators.
→ Simplify fraction to lowest term by dividing both
numerator and denominator by the GCF.
→ Change mixed number into improper fraction/
whole number into proper fraction.
→ Take the reciprocal of the divisor.
→ Multiply both numerators.
→ Multiply both denominators.
→ Simplify fraction to its lowest term.
108
PROJECT MIMs Grade 7
II. Perform the indicated operation. Write your answer on a separate
sheet of paper. Show your complete solution.
1.



2.


3.



4.



5.

Reinforcement
Choose the letter of the correct answer. Then write it on a separate sheet
of paper.
1. What will be the product of


and
?
A.


B.


C.

D.
2. Find the value of N in



.
A.
B.


C.


D.


3. Which expression is equal
?
A.


B.

C.
D.
4.
. What is the value of N?
A.
 B.
C. 
D. 
5. An electric wire measures 5
meters. It is divided into 5 equal parts.
How long is each of the 5 wires?
A.
m B.
m C.

m D.

m
109
PROJECT MIMs Grade 7
CHALLENGE
Read and analyze the given problem. Write your answer on a separate
sheet of paper. Show your complete solution.
1. Marvin bought 6 basketballs. Each ball weighs


kg. What is the total
weight of the 6 basketballs? Express your answer in mixed numbers.
2. A certain fraction divided by
gives the answer

. What is the
value of that fraction?
110
PROJECT MIMs Grade 7
G7 MIMs # 17 – WEEK 6 – 1
st
QUARTER
OPERATION ON RATIONAL NUMBERS
Square root is “one” of the two equal factors of a number.
Examples
36 = 6 x (6), therefore the square root of 36 is 6.
36 = (-6) x (-6), then -6 is also the square root of 36.
81 = 9 x (9), that means 9 is the square root of 81.
81 = (-9) x (-9), therefore -9 is the square root of 81.
►Principal root is the positive root of a number to distinguish it from the
negative value. That means the principal root of 36 is +6 and the principal
root of 81 is +9.
Note: If we are asked to give the square root of a number, we normally
give only the principal root.
►The square root of a number may be a rational number or irrational
number.
▪Rational numbers- any number which can be expressed as a ratio or
quotient between two integers where the denominator is not zero.
▪Irrational numbers- are numbers that cannot be made by dividing two
integers. It is the opposite of rational numbers.
Examples
Given
Principal Root
Rational or Irrational
1.
√
144
12
Rational
2.
√
0.25
0.5
Rational
3.
√
5
2.449489..
Irrational
4.
√
50
7.071067..
Irrational
5.π
3.1415926..
Irrational
LEARNING COMPETENCY - Describe principal roots and tells whether they
are rational or irrational.
OBJECTIVES – Identify numbers as to rational or irrational number.
Determine the square root of a number.
111
PROJECT MIMs Grade 7
Write your answer on a separate sheet of paper. Show your complete
solution.
I. Give the principal root of each of the following:
1.
√
100 4.
√
900
2.
√
256 5.
√
1296
3.
√
625
II. Write RN if the root is a rational number and IN if it is an irrational
number.
_____1.
√
100 _____4.
√
289
_____2.
√
160 _____5.
√
40
_____3.
√
225
Reinforcement
Choose the letter of the correct answer. Then write it on a separate sheet
of paper.
1. What is the square root of 196?
A. 14 B. 16 C. 18 D. 24
2. The square root of the sum of 69 and 31 is a/an _________.
A. Rational number C. Both rational and irrational
B. Irrational number D. Neither rational nor irrational
3. The area of a square is 169 sq. units. What is the measure of each side?
(Note: Area of square = side x side)
A. 13 B. 14 C. 15 D. 16
4. Which is not a rational number?
A.
√
324 B.
√
100 C.
√
1000 D.
√
10000
5. One of the two equal factors of a certain number is 25. What is the
number?
A. 5 B. 25 C. 215 D. 625
CHALLENGE
Read and analyze the given problem. Write your answer on a separate
sheet of paper. Show your complete solution.
A number that has 2 equal factors is considered a perfect square.
Identify all perfect squares from 1 to 400 then give their square roots.
112
PROJECT MIMs Grade 7
G7 MIMs # 18 – WEEK 6 – 1
st
QUARTER
PRINCIPAL ROOTS AND IRRATIONAL NUMBERS
If the square root of a number is a rational number, then that number is a
perfect square number. In the given examples below, 4, 9, 16, 25, and 36
are all perfect squares because their square roots are rational numbers.
Examples
Given
Two Equal Factors
Square Root
4
2 · 2
2
9
3 · 3
3
16
4 · 4
4
25
5 · 5
5
36
6 · 6
6
What if you have to get the square root of a number that is not a perfect
square?
Examples
1.
√
6 = ?
6 is not a perfect square. It only means that its square root is not a rational
number (not exact). What should you do to get the answer?
First, identify the nearest perfect square number smaller than the given and
the nearest perfect square that is bigger than the given. The answer is an
irrational number between the square roots of the two identified perfect
squares.
▪ 4 is the nearest perfect square number that is smaller than 6.
▪ 9 is the nearest perfect square number that is bigger than 6.
Study the diagram. It will show us the answer.
√4
√6
√9
2
3
LEARNING COMPETENCY - Determine between what two integers the
square root of a number is.
OBJECTIVE - Determine between what two integers the square root of a
number is.
113
PROJECT MIMs Grade 7
If the square root of 4 is 2 and the square root of 9 is 3, it shows
that the square root of 6 is between 2 and 3.
2.
√
34 = ?
The two perfect square numbers nearest to 34 are 25 and 36.
If
√
25 = 5 and
√
36 = 6, then it follows that
√
34 is between 5 and
6.
Note: PSN means Perfect Square Numbers
Therefore,
√
34 is between 5 and 6.
3. Between what two whole numbers does
√
87 lies?
Therefore,
√
87 lies between 9 and 10.
Between what two numbers can you find the following? Write your answer
on a separate sheet of paper. Show your complete solution.
1.
√
40 _____ 6.
√
340 _____
2.
√
102 _____ 7.
√
450 _____
3.
√
175 _____ 8.
√
560 _____
4.
√
237 _____ 9.
√
630 _____
5.
√
295 _____ 10.
√
740 _____
√
25
√34
√36
PSN Given PSN
5
6
N
√81
√87
√100
9
N
10
114
PROJECT MIMs Grade 7
Reinforcement
Between what two numbers can you find the following square roots? Match
column A with corresponding answer in column B. Write your answer on a
separate sheet of paper.
CHALLENGE
Read and analyze the given problem. Write your answer on a separate
sheet of paper. Show your complete solution.
A square lot has a land area of 2400 sq. m. between what two whole
numbers in meters is the measure of each side of the square lot?
Column A
1.
√
15
2.
√
58
3.
√
102
4.
√
200
5.
√
38
Column B
A. Between 6 and 7
B. Between 7 and 8
C. Between 10 and 11
D. Between 3 and 4
E. Between 4 and 5
F. Between 5 and 6
G. Between 14 and 15
115
PROJECT MIMs Grade 7
G7 MIMs # 19 – WEEK 7 – 1
st
QUARTER
ESTIMATING SQUARE ROOTS
Examples
1. Estimate the
 to the nearest hundredths.
A. Identify the lowest perfect square near
 and the greatest
perfect square near
.
In this case we have


. Which means 3 is the lowest
perfect square near
 and 4 is the greatest perfect square
near

Taking the square root of a number is like doing the reverse operation of
squaring a number. For example, both 7 and -7 are square roots of 49 since
= 49 and 󰇛󰇜
= 49.
Integers such as 1, 4, 9, 16, 25 and 36 are called perfect squares.
Rational numbers such as 0.16,

and 4.84 are also, perfect squares.
Perfect squares are numbers that have rational numbers as square roots.
The square roots of perfect squares are rational numbers while the square
roots of numbers that are not perfect squares are irrational numbers.
If a principal root is irrational, the best you can do for now is to give an
estimate of its value. Estimating is very important for all principal roots that
are not roots of perfect nth powers.
LEARNING COMPETENCY - Estimate the square root of a whole number to
the nearest hundredth.
OBJECTIVE: Estimate the square root of a whole number to the nearest
hundredth.
116
PROJECT MIMs Grade 7
o
and
 which means
 is between the
consecutive integers 3 and 4.
B. Then follow the formula:


o


C. Convert
into decimal.
o

o Since we are estimating to the nearest hundredths, then
we have 0.14.
D. As stated earlier,
 is between the consecutive integers 3
and 4. Therefore,
 .
2. Estimate the
 to the nearest hundredths.
A. Identify the lowest perfect square near
 and the greatest
perfect square near
.
o In this case we have


. Which means 9 is the
lowest perfect square near
 and 10 is the greatest
perfect square near

o
 and
  which means
 is between
the consecutive integers 9 and 10.
117
PROJECT MIMs Grade 7
B. Then follow the formula:


o




C. Convert


into decimal.
o



o Since we are estimating to the nearest hundredths, then
we have 0.74.
o Therefore,
≈ 9.74.
Estimate the square root of the following to the nearest hundredth. Write
your answer on a separate sheet of paper. Show your complete solution.
1.
 3.
 5.
 7.
 9.

2.
 4.
 6.
 8.
 10.

Reinforcement
Choose the letter of the correct answer. Then write it on a separate
sheet of paper. Approximate the following to the nearest hundredths.
1.

A. 
B. 
C. 
2.

A. 
B. 
C. 
3.

A. 
B. 
C. 
4.

A. 
B. 
C. 
5.

A. 
B. 
C. 
CHALLENGE
Read and analyze the given problem. Write your answer on a separate
sheet of paper. Show your complete solution.
1. Find the difference
 -

2. Find the sum
 and
.
118
PROJECT MIMs Grade 7
G7 MIMs # 20 – WEEK 7 – 1
st
QUARTER
PLOTTING IRRATIONAL NUMBERS
“WHERE AM I?!”
The first step in graphing any group of numbers on a number line is
figuring out their order. It works just like alphabetizing but with numbers;
start with the smallest number, which is like starting with the letter A. Using
the examples that were given below, square root of 2 would come first,
then square root of 5, then pi. This is what it would look like on a number
line.
Notice how the red tick marks aren't on the whole number tick marks.
All irrational numbers are decimals, so they fall in between the whole
numbers.
When the first number of the decimal portion of the irrational number is
less than 5, the tick mark made on the number line should be closer to the
whole number part of the irrational number.
When the first number of the decimal portion of the irrational number is
greater than 5, the tick mark made on the number line should be farther
away from the whole number part of the irrational number.
What if the first number of the decimal portion of the irrational number is
exactly 5? Then the tick mark will be exactly halfway between the whole
number part of the irrational number and the next whole number on the
number line.
LEARNING COMPETENCY - Plot irrational numbers (up to square roots)
on a number line.
OBJECTIVE: Plot irrational numbers (up to square roots) on a number line.
119
PROJECT MIMs Grade 7
Here’s how to plot irrational numbers (up to square roots) on a number
line.
Examples
Locate and plot each square root on a number line.
Note: The non-negative positive square root of a number is called its
Principal Root.
1.
√
3
2.
√
21
3.
√
87
Plot the following square root on the number line. Write your answer on
a separate sheet of paper.
1.
√
39 6.
√
295
2.
√
75 7.
√
356
3.
√
137 8.
√
455
4.
√
190 9.
√
490
5.
√
240 10.
√
560
This number is between 1 and 2,
principal roots of 1 and 4. Since 3 is
closer to 4 than 1.
√
3 is closer to 2.
Plot
√
3 closer to 2.
This number is between 4 and 5,
principal roots of 16 and 25. Since
21 is closer to 25 than 16.
√
21 is
closer to 5. Plot
√
21 closer to 5.
This number is between 9 and 10,
principal roots of 81 and 100. Since
87 is closer to 81 than 100.
√
87 is
closer to 9. Plot
√
87 closer to 9.
120
PROJECT MIMs Grade 7
Reinforcement
Which point on the number line below corresponds to which square
root? Write your answer on a separate sheet of paper. Show your
complete solution.
1.
√
57
2.
√
6
3.
√
99
4.
√
38
5.
√
11
CHALLENGE
Plot the square root in the number line. Write your answer on a separate
sheet of paper. Show your complete solution.
1.
√
18
2.
√
175
3.
√
230
121
PROJECT MIMs Grade 7
G7 MIMs # 21 – WEEK 5 – 1
st
QUARTER
REAL NUMBER SYSTEM
► The diagram above shows the real number system where every set
seen below another set is just a subset.
► The set of natural numbers is below the set of whole numbers which
means the set of natural numbers is a subset of the set of whole numbers.
► The set of whole numbers and the set of negative numbers are both
connected and under the set of integers which means that they are both
subsets of the sets of integers. We can also conclude in the diagram that the
set of integers is the union of the set of whole numbers and negative
numbers.
Examples
Counting/Natural Numbers - These are the numbers we use in counting
things. {1, 2, 3, 4, 5 . . .}
Whole Numbers - These are numbers consisting of the set of natural or
counting numbers and zero. {0, 1, 2, 3, 4, 5…}
Integers - these are the result of the union of the set of whole numbers and
the negative of counting numbers. {…-3, -2, -1, 0,1, 2, 3…}
Rational Numbers - are numbers that can be expressed as a quotient of
two integers. The integer a is the numerator while the integer b, which cannot
be 0 is the denominator. This set includes fractions and some decimal
numbers.{ 0.50,
, 4.33, 62,
}
LEARNING COMPETENCY - Illustrate the different subsets of real
numbers.
OBJECTIVE - Describe and illustrate the real number system.
122
PROJECT MIMs Grade 7
Irrational Numbers - are numbers that cannot be expressed as a quotient
of two integers. Every irrational number may be represented by a decimal
that neither repeats nor terminates. {,
  9.121345..}
Tell whether the statement below is TRUE or FALSE. Write your answer on
a separate sheet of paper.
1. -4 belong to the set of whole numbers.
2. The set of rational numbers is a subset of the set of integers.
3. When “zero” is added to the set of natural numbers, it becomes the set
of whole numbers.
4. Rational numbers combined with irrational numbers, the result is the set
of real numbers.
5. Rational numbers may be expressed as a fraction, ratio, or quotient of
two numbers a/b where b ≠ 0.
6. √4 is a rational number.
7. {1, 2, 3, 4, 5,…} is the set of whole numbers.
8. 2/5 and 1.4 are both elements of the set of real numbers.
9. The value of π is approximately 3.14 to the nearest hundredths.
10. 2/9 is equal to 0.2222…, a repeating, non-terminating decimal.
Reinforcement
Identify whether the given number is an element of each of the different sets
of number. Then write your answer in a separate sheet of paper
Given
Natural
Numbers
Whole
Numbers
Integers
Rational
Numbers
Irrational
Numbers
Real
Numbers
Ex. +3
√5
1. 2/5
2. -9
3. √49
4. 1.42
5.
CHALLENGE
Make your own diagram/flow chart about the real number system. Write
your answer on a separate sheet of paper.
123
PROJECT MIMs Grade 7
G7 MIMs # 22 – WEEK 8 – 1
st
QUARTER
REAL NUMBERS IN ORDER
The real numbers are ordered in nature; and are ordered in such a way that
one is greater or less than the other. We can say that for any two different
numbers a and b, one and only one of the following is true:
(1) a is less than b; (2) a is equal to b; or (3) a is greater than b.
Using the number line, LEFT is LESS and RIGHT is MORE or GREATER.
The farther the negative number from 0, the lesser its value, and the farther
the positive number from 0, the higher its value.
Examples
1. Rewrite 3, -3, 0 in increasing order.
Answer: Since the order is increasing we will start with the least value to the
greatest value, so we have -3, 0, 3.
2. Consider the number line, then rewrite
, -0.25, 0.5 and -1.33 in
ascending order.
Answer: Since ascending is increasing, we order the numbers from the
least value to the greatest value, we have -1.33, -0.25, 0.5,
.
3. Rewrite 1.25,
,
in decreasing order.
Answer: This time, the easiest way for you to check the order of such
numbers is to convert it all in decimals.
LEARNING COMPETENCY - Arrange real numbers in increasing or
decreasing order.
OBJECTIVE: Arrange real numbers in increasing or decreasing order.
124
PROJECT MIMs Grade 7
1.25 is already in decimal

= 3.5 for fraction, you need to divide the numerator by the
denominator
≈ 2.45 if the number is not squared, then assume its
value by determining two numbers that it is in between.
is
between 2 and 3.
Note: The symbol “ means approximately equal.
Since what is asked is decreasing, we order the number from the greatest
value to the least value so we have
,
, 1.25.
Note: Your answer must be the given numbers, and NOT it converted
decimal.
4. Rewrite
, -1.23,
,
, 1 and
in descending order.
Answer: Converting some of the numbers in decimals, we have:
= 0.75,
≈ 1.41 or between 1 and 2,
= -0.6,
= 1.14, -1.23, 1
Since we have to write it in decreasing order, we start with the greatest
value to the least value so we have
,
, 1,
,
, -1.23
Perform what is asked. Write your answer on a separate sheet of paper.
1. Rewrite -5, 15, -10, 0, and 10 in increasing order.
2. Rewrite 6.3, -8, -7.6, and -1.75 in ascending order.
3. Rewrite 1.23, -1.03, 1, and -2.04 in decreasing order.
4. Rewrite
,
,
and
in decreasing order.
5. Rewrite
, 2,
and
 in descending order.
6. Rewrite


 in increasing order.
7. Rewrite


 in decreasing order.
8. Rewrite   

 in ascending order.
9. Rewrite 


 in descending order.
10. Rewrite




in increasing order.
125
PROJECT MIMs Grade 7
Reinforcement
Choose the letter of the correct answer. Then write it on a separate sheet
of paper.
1. Which number has greatest value?
A. 5 B. -2 C. 10 D. -4
2. Which statement is always true?
A. -2.5 is greater than -0.3
B. Real numbers are not in ordered.
C. Positive fractions are greater than negative decimals.
D. Some negative numbers are greater than the positive numbers.
3. Arrange the numbers in increasing order E=
, F = -3.34, G = 2,
H = -5.2
A. E, G, F, H C. H, F, E, G
B. H, F, E, G D. G, E, F, H
4. Which number has the least value?
A. 
B. 0 C. -7.45 D. -1.6
5. Which is next to 2.5, 0, -1.52, ___?
A. -0.57 B. -2.52 C. -1.09 D. -1.5
CHALLENGE
Write your answer on a separate sheet of paper. Show your complete
solution.
Plot A = -3, B =
, C =
, D =
, E = 3, F =
and G = 0 on
a number line.
126
PROJECT MIMs Grade 7
G7 MIMs # 23 – WEEK 8 – 1
st
QUARTER
Real Numbers in Order
Real Number System has different subsets. It may be represented on a
number line.
Subsets of the Set of Real Numbers
Knowing where the subsets of real numbers are located, we may arrange
them accordingly in increasing or decreasing order.
Examples
1. Arrange the following numbers in increasing order.
{4, -1,
, 0.5,
}
{
 
 󰇞
One way to arrange the numbers in increasing order is by plotting them on
the number line.
After plotting the numbers on the number line, we can now arrange the
numbers in increasing order from left to right. The proper arrangement will
be {
, -1, 0.5,
, 4 }.
LEARNING COMPETENCY - Arrange real numbers in increasing or
decreasing order.
OBJECTIVE: Arrange real numbers in increasing or decreasing order
Note:


127
PROJECT MIMs Grade 7
2. Arrange {
,
,
,
,} in decreasing order.
In this example, there are numbers that can be simplified before plotting on
the number line.
is equal to 3,
is 
, and
is 2. Now, we can plot
them on the number line.
So, the proper arrangement will be {
,
,
,
,}.
Plot the following numbers on the number line below. Then arrange in
ascending order. Write your answer on a separate sheet of paper.
{


,
,
 ,

,

}
Reinforcement
Choose the letter of the correct answer. Then write it on a separate sheet
of paper.
1. Which of the following is the correct arrangement of {-4, 2, -12, -7,0} if
arranged in increasing order?
A. {-4, -12, 0, -7, 2} C. {-12, -7, -4, 0, 2}
B. {-7, -4, 0, 2, -12} D. {-12, -7, -4, 2, 0}
2. If arranged in descending order, which is the correct arrangement of
{,
,
 ,
,

}?
A. {
,
, ,
,

} C. {
,,
 ,
,

}
B. {
 ,
,

,
, } D. {
,
,,
 ,

}
3. What will be the last number if {

,
,
 ,

,} is arranged
in decreasing order?
A.
 B.

C.

D.

4. If arranged in ascending order, what will be the first number in the set of
{

, - 4,
,
, ,
} ?
A.
 B.
 C.

D.
128
PROJECT MIMs Grade 7
5. Which of the sets is arranged increasingly?
A. {,
,
 ,

, } C. {,
,

,

,

}
B. {
,,

,
, 17} D. {
,
,  , }
CHALLENGE
Arrange the sets in descending order. Write your answer on a separate
sheet of paper. Show your complete solution.
1. {

󰇞
2. {
 






}
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